"To keep the majority" means to retain or maintain control or power over a group or situation by having more people on your side than anyone else. Full definition
These accessories will help keep the majority of dirt and moisture contained while keeping your entryway clean and your floors damage free. (lifestorage.com)
You get the pleasure and pride of being a published author while keeping a majority of every sale you make! (nancyhendrickson.com)
Therefore, too keep the majority happy, the council will be mostly Christian. (religion.blogs.cnn.com)